Can Game Theory Explain Cooperation?

I must begin this blog post with a confession. I have never been into game theory, and although I did take some undergraduate courses in it, I’ve always struggled to understand it all. But while I was somewhat uneasy about game theory (or at least parts of it), I couldn’t express the reasons for my reservations. It was more of a feeling.

From these days, I still remember a conversation I had with a fellow undergrad (perhaps she had also recently graduated) about game theory. She was rather fond of it and gave nice arguments about why it was helpful and good. Back then, one of the criticisms I voiced was that game theory struggled to explain cooperation, or so I thought.

What made me wonder was how exactly game theory could explain cooperation if it assumes that people are selfish and maximize their (narrowly construed) expected utility. She responded, “Oh, that’s not a big deal. Once you assume iterated games, it is rational to cooperate.” In and of itself, the answer seemed convincing. After all, if we anticipate seeing each other more than once, we should adjust our behaviour accordingly. And then it may really be “rational” to cooperate and not defect. So, that day, I left it at that. But I couldn’t quite shake off a feeling of uneasiness with that solution.

Things changed when I read Joe Henrich’s monumental work The WEIRDest People in the World, published in 2020. Henrich does many things in this tract, but he also touches on life in prehistoric times. And in an intriguing passage, he reflects on interactions between humans. Henrich (p. 303) writes:

WEIRD people tend to think that trade is straightforward: we have wild yams and you have fish; let’s swap some yams for some fish. Easy. But, this is misguided. Imagine trying to barter yams for fish in the hunter-gatherer world described by William Buckley in Australia. In this world, other groups were often hostile, and strangers were frequently killed on sight. To conceal their nocturnal locations, bands erected low sod fences around their campfires so they couldn’t be spotted from a distance. If I showed up at your campfire with some yams to trade, why wouldn’t you just kill me and take them? Or you might have thought we are only offering our toxic yams, which would slowly poison you and your band. Under such conditions, which were probably common over our species’ evolutionary history, it’s difficult to see how smoothly flowing trade could ever emerge.

If Henrich is right, then we cannot simply assume that there will be a second round, not to speak of games with infinite rounds. Indeed, perhaps the usual kind of interaction would be the attempt to kill each other. Or the two would refrain from interacting with each other at all.

But if, for this or that reason, there were a second round, that would presuppose that there was a first round of interaction and that it had been peaceful. For example, we had exchanged yams for fish. To the least, we did not kill each other, either with our spears or poisoned yams. But this is, or at least is very close to, cooperation in the sense of peaceful, coordinated, and reciprocal interaction—if only in a very crude and basic form.

Following Henrich, then, the sheer fact that there is a second round of interaction, that is, that our game started at all, and if it started that it does not end after the first instance (because either I killed you or you killed me, or to the least, the interaction was so distasteful that none of us sees any reason to interact with each other again), requires a basic level of cooperation.

But this implies that game theorists’ assumption of iterated games to demonstrate that cooperation is possible and does, indeed, follow in game-theoretic scenarios, is a petitio. They already assume that people’s interaction will be characterized by basic cooperation or at least peacefulness when they assume that people will face iterated and even infinitely iterated games, that is, do not kill each other at first sight. Therefore, game theory covertly assumes cooperative and peaceful interaction to explain cooperation. And that’s problematic.

I want to come back to the remarks I made at the beginning of this piece. I am by no means an expert in the field of game theory. I am just an outsider who puts forward his thoughts about game theory—a critic who, surely, may miss the forest for the trees. But perhaps commenters on this blog can show me where my reasoning goes wrong. Or, perhaps, my critique has something to it, and game theory has some work to do.

 


Max Molden is a PhD student at the University of Hamburg. He has worked with European Students for Liberty and Prometheus – Das Freiheitsinstitut. He regularly publishes at Der Freydenker.

READER COMMENTS

rick shapiro
Dec 28 2024 at 1:02pm

The fact that pre-modern tribes often developed hostile relations with their neighbors does not imply that they were universally hostile to outsiders. Many European explorers documented friendly treatment by newly discovered people. See also how Herodotus described the means by which Carthaginians traded with a coastal African tribe with which they had no common language.

Many non-human animals have agency, if not the ability to philosophize. Robert Axelrod used iterated prisoner’s dilemma to model how ‘tit for tat’, rather than ‘always attack’ is an evolutionarily stable strategy.

Max Molden
Dec 30 2024 at 4:14am

I’m in total agreement with you on that, Rick. My main concern is simply how you can explain this emergence of cooperation in game theory. Why is there an iterated game in the first place? Explaining this cannot be done by assuming there is an iterated game. For this means you assume cooperation or at least something very close to it. Put differently, if, within game theory, you cannot just assume there is an iterated game, how then can you explain cooperation within this framework?

rick shapiro
Dec 30 2024 at 1:08pm

The model of altruism (or at least bourgeois behaviors like territoriality) via iterated prisoner’s dilemma makes no assumptions about multiple interactions between two individuals. It works because, in a breeding population, those with the cooperation trait acquire more benefits than the non-cooperators, even though any specific non-cooperator acquires more benefits than are acquired by the cooperator from the interactions of those two specific individuals. More total benefits from the totality of interactions accrue to tit-for-tat cooperators if there are even a few of them in the population.

Peter
Dec 29 2024 at 4:51am

Game theorist here. That the game ends if we don’t cooperate is perfectly consistent with the usual model. We don’t usually teach it that way, but perhaps we should.

All the theory needs is that: if we cooperate, we can (and will, in equilibrium) cooperate again; and if I defect, I’m punished. But the punishment can be many things. The game ending is a punishment: no more opportunities for beneficial cooperation. That’s enough. (In principle. Whether we actually predict cooperation will depend on parameters, as always.)

So in your example, all we need to believe to get cooperation going is that the value of cooperating forever is higher than the value of killing the stranger on first sight. No further punishment and no repetition after defection required.

Max Molden
Dec 30 2024 at 4:34am

Peter, thanks for your comment! Yes, if the players believe the value of cooperating forever is higher than that of total defection (i.e., killing), they will cooperate. But then I’m uneasy with this as a successful explanation for cooperative behaviour within game theory because one basic assumption, as far as I know, is that defecting always is superior to cooperating if the other cooperates. How can you then explain that people, although this is true/a basic assumption, would believe that cooperating is better for them? For this, you’d somehow need an exogenous explanation of how people overcome the free-rider incentive.

I should add I’m not taking this to be really a criticism of GT, but rather showing that it struggles at explaining cooperation.

Matthias
Dec 29 2024 at 5:28am

Game theory doesn’t predict that 100% reliably predicted iterations are necessary for cooperation. It’s just an observation that when iterations are expected, cooperation tends to happen in something like a prisoner’s dilemma.

So your friend brought that up, because it’s easy to summarise and explain.

Emergence (or non-emergence!) of cooperation under various conditions is an interesting subject to study, and you can use game theory for it.

Btw, settled people with agricultural would have more of an expectation of repeated interaction, just because population density tends to be higher.

Max Molden
Dec 30 2024 at 4:37am

Thanks for your thoughts, Matthias! You write that “when iterations are expected, cooperation tends to happen in something like a prisoner’s dilemma.” But this is just my concern: here, you assume that iterations are expected. So you do not explain cooperation but rather show what happens given that people cooperate. Game theory then needs to rely on an exogenous explanation for why people expect iterations in the first place. These explanations exist, but relying on them by assuming there are iterated interactions implies that GT doesn’t explain the emergence of cooperation.

David Seltzer
Dec 29 2024 at 10:26am

Max: Nice stuff here. I think the second iteration proceeds from either tribe’s assessment of the risks of conflict in the initial meeting. The tribe with the fish understands there is no guarantee they won’t be attacked by the yam tribe. They will come prepared for battle. In both cases there is implied private ownership of yams and fish. It seems the incentive is to trade rather than risk being killed by the other. Of course, I could be wrong.

Max Molden
Dec 30 2024 at 4:44am

David, thanks for your comment and your kind words! I find it difficult to assess how people overcame the incentive to defect/kill at first sight. (We (luckily) somehow achieved this.)

My main point is that game theory assumes this and thus cannot offer the explanation for the emergence of cooperation which you attempt. (But looking at explanations for how we were able to cooperate, what role private ownership played in this is really interesting. Perhaps something for a future blog post!)

Mactoul
Dec 30 2024 at 10:14pm

Neighboring band is likely to be kin as well. So you have loose  networks of kins extending over large distances.  With such kinship there is always intermarrying going on. So you have iteration biologically imposed.

David Seltzer
Dec 31 2024 at 12:25pm

Mactoul: I hadn’t thought about intermarrying between tribes. Nice insight.

Mactoul
Dec 30 2024 at 12:08am

Humans are patrilocal, like chimpanzees,  and this provides another facet to cooperate-compete dynamics. In patrilocal species the males stay put and the females move at puberty to another band. Females may be captured by raiding (a constant in history) or by exchanges.

The cooperate-compete dynamics works within a band too.  Here JBS Haldane’s quip about laying down one’s life for two brothers or eight cousins provides the framework for understanding.

Max Molden
Dec 30 2024 at 4:48am

I learned a new word here (patrilocality), thanks a lot, Mactoul! Could you point me to an accessible work of Haldane which elaborates on what you mention as his quip?

Mactoul
Dec 30 2024 at 10:09pm

I would rather recommend Richard Dawkins’ The Selfish Gene for kin altruism and game theory in evolution. It is very readable.

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